# Borel set, criterion for a

A necessary and sufficient condition for an $\mathcal{A}$-set in a complete separable metric space to be a Borel set. Two criteria can be stated as follows: 1) its complement must also be an $\mathcal{A}$-set (Suslin's criterion); and 2) it can be represented as the union of non-intersecting components (Luzin's criterion).